The unstable spectrum of swirling gas flows
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چکیده
The asymptotic structure of the discrete spectrum of a compressible inviscid swirling flow with arbitrary radial distributions of density, pressure and velocity is described for disturbances with large wavenumbers. It is shown that discrete eigenmodes are unstable when a criterion derived by Eckhoff & Storesletten (1978) is satisfied. In general, these modes are characterized by a length scale of order |m|−3/4 where |m| 1 is the azimuthal wavenumber of the disturbance. They have a spatial structure similar to the incompressible modes obtained by Leibovich & Stewartson (1983). In the particular case of solid-body rotation with a positive gradient of entropy, the unstable discrete spectrum contains modes which scale with |m|−1/2. If the modes are localized near a solid boundary, they scale with |m|−2/3.
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تاریخ انتشار 2005